- 03-19 D.Benedetto, F. Castella, R. Esposito, M. Pulvirenti
- Some Considerations on the derivation of the nonlinear
Quantum Boltzmann Equation
(663K, Postscript, Pdf)
Jan 17, 03
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Abstract. In this paper we analyze a system of $N$ identical quantum particles in a
weak-coupling regime. The time evolution of the Wigner transform of the
reduced density matrix is represented by means of a perturbative
The expansion is obtained upon iterating the Duhamel formula.
For short times, we rigorously prove that a subseries of the latter,
converges to the solution of the
equation which is physically relevant in the context.
In particular, we recover the transition rate as it is predicted by Fermi's Golden
However, we are not able
to prove that the quantity neglected while retaining a subseries of the complete
perturbative expansion, indeed vanishes in the limit: we
plausibility arguments in this direction.
The present study holds in any space dimension $d\ge 2$.